3 problems

Let $r\geq 4$ and consider the outer space of rank-$r$ free groups equipped with the entropy metric. Finite-diameter conjecture. The entropy metric has finite diameter on the outer…

Let $r\geq 3$. A metric graph of rank $r$ has unit entropy when its entropy is normalized to equal $1$, and a subgraph is proper when it is a strict subgraph of the graph. Uniform…

Let $X_n$ be outer space, let $\mathrm{Out}(F_n)$ act on it naturally, and let $ds^2$ and $ds^2_{\varepsilon}$ be the two Riemannian metrics defined in the previous section. The qu…